I’ll try to get through your questions here. But, I’m not a philosophy major.

Rh1no1;
What I would like to ask you after this reply, is this: Is atheism based on the belief that faith, or anything yet concretely proven, is merely hypothesis and should not be respected, valued, or adhered to?

I can’t speak for all atheists. But, even in science, there is the matter of “probabilities”. Hypothesis’ typically begin on a hunch, which theory “smells good”. With more data gathered, a hypothesis can either show a low probability or high probability of being correct when tested. Monkeys might evolve the ability to fly someday. But, it looks improbable. Nothing supports that hypothesis. So, its not even entertained.
In quantum physics, the Heisenberg uncertainty principle is a mathematical limit on the accuracy with which it is possible to measure everything there is to know about a physical system. In its simplest form, it applies to the position and momentum of a single particle, and implies that if we continue increasing the accuracy with which one of these is measured, there will come a point at which the other must be measured with less accuracy.

Wouldn’t this go against the claim that atheist have which is that they have a right NOT to believe?

Everyone has right to believe whatever they like, no matter how ridiculous. But, when false claims and imaginary deities do demonstrable harm to society, or promote ignorance of what is true, those claims must be challenged.
Atheism isn’t a church with its own dogma. The point of atheism, as far as I know, is to spend less time and resources chasing false hopes, exercise the higher brain faculties and use reason to find what is demonstrably true. This would enable humanity to make improvements in the future that we lacked in the past.

It something has a connection to your heart rather than to a ruler and a scientific principal, does it make that belief any less important or valuable than one that can be re-proven in a jar?

In what context? if my heart tells me to do something that is demonstrably horrific (like barbecuing the neighbor’s kids for laughs) its a safe bet the evidence trumps my heart.
On the other hand, listening to your heart can trump perfectly rational situations and you may sacrifice yourself, acting against your own self-interest for a higher purpose and the greater good.

Is a girl’s belief in a unicorn (or God) any less valuable than, say, the theory or relativity or the speed of light?

The Theory of Relativity or Unicorns or God has no bearing on morality, if that’s what you’re getting at. Conscience is a product of our evolution as a species, both biologically and socially. Even primates and other animals are capable of empathizing with others.

Which one helps her survive best?

Neither.

What is the qualification?

To survive humans need food, water, and oxygen.
If you mean what helps her remain sane and healthy, that’s another subject.

And you’re right, religion is sometimes illogical, but sometimes it is not. If this is not really an argument about which belief is right, and which one is wrong, is it simply about one’s right to choose what to believe?
If so, then why the argument?

Following the September 11, 2001 attacks, when asked how the world might have changed, biologist Richard Dawkins responded:

Many of us saw religion as harmless nonsense. Beliefs might lack all supporting evidence but, we thought, if people needed a crutch for consolation, where’s the harm? September 11th changed all that. Revealed faith is not harmless nonsense, it can be lethally dangerous nonsense. Dangerous because it gives people unshakeable confidence in their own righteousness. Dangerous because it gives them false courage to kill themselves, which automatically removes normal barriers to killing others. Dangerous because it teaches enmity to others labeled only by a difference of inherited tradition. And dangerous because we have all bought into a weird respect, which uniquely protects religion from normal criticism. Let’s now stop being so damned respectful!

What is the argument?

What is the harm done by belief in the supernatural? and Is it worth continuing to promote this belief without something to substantiate it on?

Can you define it using one sentence?

Is there or is there not a God and, if so, which one?

There are so many layers of abstract. Nothing in life is as concrete to me as the abstract notion of love. It’s hard to argue a paradox. Are we all talking over one another or do we meet somewhere in here, perhaps on a more universal level? As usual.. philosophy asks more questions than it answers.

Yes it does.

I think I stated in one of my videos that I tried to define my philosophy toward religion by saying I am an Existential Zen Buddhist Atheist. I kinda got into Buddhism (as philosopher Alan Watts called it, “The Religion of No Religion”), in a strange way, by reading up on physics.